+386
We have the following:
Triangle with sides "a" "b" "c" (c being the hypotenuse)
hypotenuse = c = 15cm
there is 3 cm of difference between a and b
so let's say
a = b - 3
b = a - 3
Pythagorean theorem: a^2 + b^2 = c^2
replace:
a^2 + (a-3)^2 = 15
Where do you go from there to find a and b ?
+129840 Note ......we can't have that
a = b −3 and b = a − 3
Rearranging the first, we have that b = a + 3
But b can' t equal a − 3 and a + 3 at the same time !!!
So...I will assume that b = a − 3
a^2 + (a-3)^2 = 15 expand
a^2 + a^2 − 6a + 9 = 15
2a^2 − 6a − 6 = 0
a^2 − 3a − 3 = 0 the only solution to this that makes sense is that a = [ 3 + √21 ] / 2 cm
And b = a − 3 = [ 3 + √21 ] / 2 − 3 = [ − 3 + √21 ] / 2 cm
+386 Here are the solutions from the book:
One side is 9cm and the other 12cm.
Also, I think you forgot to square the hypotenuse when starting. That might be the problem...
+129840 Ah....I missed that......shame on me......let me try again........!!!
a^2 + (a-3)^2 = 15^2 expand
a^2 + a^2 − 6a + 9 = 225 simplify
2a^2 − 6a − 216 = 0 divide by 2 on both sides
a^2 − 3a − 108 = 0 factor
(a − 12 ) ( a + 9) = 0
Set both factors to 0 and the only solution to this that makes sense is that a = 12 cm
And b = a − 3 = 12 − 3 = 9 cm
+386 I get what you're doing but how can I put this into maths:
Set both factors to 0 and the only solution to this that makes sense is that a = 12 cm
